1. Field of the Invention
The present invention relates to an angle demodulation device and method using the same, particularly to a periodically resetting integration angle demodulation device and a method using the same.
2. Description of the Related Art
An optical sensing system is a sensor to measure acceleration, including those of a piezoresistive pressure sensor, a capacitive sensor, a piezoelectric sensor and an optical sensor, especially the optical sensor with better sensitivity. The optical sensor can apply to the system of high standard without disturbance of electromagnetic radiation, such as an advanced intelligent fuse system.
Among all kinds of optical accelerometers, Path Matched Differential Interferometry (PMDI) is an effective accelerometer. Presently, there are several kinds of demodulation systems which are references to process the rear-end signals. But circuits of the system are fabricated on a circuit board by using discrete elements. A large volume of the system is not only hard to apply to an optical sensing system but also achieves a purpose of microminiaturizing a whole system. As shown in FIG. 1, the traditional technology has been provided a synthetic heterodyne demodulation circuit. Firstly, an optical fiber and an optical phase-measuring signal are modulated into an angle modulation signal by a sine wave, wherein the angle modulation signal is expressed by an equation (1):VPMDI(t)=A+B cos [φc cos(2πfct)+Δφ(t)]  (1)
Wherein A and B are constants, φc is a modulation depth, fc is a modulation frequency, Δφ(t) is an angle variation resulted from acceleration. A direct-current (DC) blocker 10 receives the angle modulation signal and filters out a DC signal of the angle modulation signal to generate an alternative-current (AC) signal. According to Fourier-Bessel theory, the AC signal is expressed by an equation (2):
                                          V            PMDI                    ⁡                      (            t            )                          =                                  ⁢                                  ⁢                  A          +                      B            ⁢                          {                                                                    [                                                                                            J                          0                                                ⁡                                                  (                                                      ϕ                            c                                                    )                                                                    +                                              2                        ⁢                                                                              ∑                                                          k                              =                              1                                                        ∞                                                    ⁢                                                                                                          ⁢                                                                                                                    (                                                                  -                                  1                                                                )                                                            k                                                        ⁢                                                                                          J                                                                  2                                  ⁢                                                                                                                                          ⁢                                  k                                                                                            ⁡                                                              (                                                                  ϕ                                  c                                                                )                                                                                      ⁢                                                          cos                              ⁡                                                              (                                                                  4                                  ⁢                                                                                                                                          ⁢                                  k                                  ⁢                                                                                                                                          ⁢                                  π                                  ⁢                                                                                                                                          ⁢                                                                      f                                    c                                                                    ⁢                                  t                                                                )                                                                                                                                                                          ]                                    ⁢                                      cos                    ⁡                                          (                                              Δϕ                        ⁡                                                  (                          t                          )                                                                    )                                                                      -                                                                  ⁢                                                                  ⁢                                                      [                                          2                      ⁢                                                                        ∑                                                      k                            =                            0                                                    ∞                                                ⁢                                                                                                  ⁢                                                                                                            (                                                              -                                1                                                            )                                                        k                                                    ⁢                                                                                    J                                                                                                2                                  ⁢                                                                                                                                          ⁢                                  k                                                                +                                1                                                                                      ⁡                                                          (                                                              ϕ                                c                                                            )                                                                                ⁢                                                      cos                            ⁡                                                          (                                                              2                                ⁢                                                                  (                                                                                                            2                                      ⁢                                                                                                                                                          ⁢                                      k                                                                        +                                    1                                                                    )                                                                ⁢                                                                                                                                  ⁢                                π                                ⁢                                                                                                                                  ⁢                                                                  f                                  c                                                                ⁢                                t                                                            )                                                                                                                                            ]                                    ⁢                                      sin                    ⁡                                          (                                              Δϕ                        ⁡                                                  (                          t                          )                                                                    )                                                                                  }                                                          (        2        )            
The AC signals V1,Lo and V2,Lo are respectively transmitted to an analogous multipliers 12 and 12′ and the AC signal V1,Lo are multiplied by cos(2πfct) and simplified by a way of product to sum to obtain an equation (3):
                                          V                          1              ,              Lo                        ′                    ⁡                      (            t            )                          =                                                                              V                                      1                    ,                    Lo                                                  ⁡                                  (                  t                  )                                            ×                              cos                ⁡                                  (                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      c                                        ⁢                    t                                    )                                                      ⇒                                          V                                  1                  ,                  Lo                                ′                            ⁡                              (                t                )                                              =                                                    C                                  1                  ,                  0                                ′                            ⁢                              sin                ⁡                                  (                                      Δϕ                    ⁡                                          (                      t                      )                                                        )                                                      +                                          C                                  1                  ,                  1                                ′                            ⁢                              cos                ⁡                                  (                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      c                                        ⁢                    t                                    )                                            ⁢                              cos                ⁡                                  (                                      Δϕ                    ⁡                                          (                      t                      )                                                        )                                                      +                                          C                                  1                  ,                  2                                ′                            ⁢                              cos                ⁡                                  (                                      4                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      c                                        ⁢                    t                                    )                                            ⁢                              sin                ⁡                                  (                                      Δϕ                    ⁡                                          (                      t                      )                                                        )                                                      +                                          C                                  1                  ,                  3                                ′                            ⁢                              cos                ⁡                                  (                                      6                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      c                                        ⁢                    t                                    )                                            ⁢                              cos                ⁡                                  (                                      Δϕ                    ⁡                                          (                      t                      )                                                        )                                                      +            …                                              (        3        )            
Then, an analogous band-pass filter 14 with central frequency f ID receives V1,Lo′(t) to generate an output signal expressed by an equation (4):V1,Lo″(t)=C′1,1 cos(2πfct)cos(Δφ(t))  (4)
Similarly, the AC signal V2,Lo(t) is multiplied by sin(4πfct) and simplified by a way of product to sum to obtain an equation (5). Another analogous band-pass filter 14′ with central frequency fc receives V′1,Lo(t) to generate an output signal expressed by an equation (6).
                                          V                          2              ,              Lo                        ′                    ⁡                      (            t            )                          =                                                                              V                                      2                    ,                    Lo                                                  ⁡                                  (                  t                  )                                            ×                              sin                ⁡                                  (                                      4                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      c                                        ⁢                    t                                    )                                                      ⇒                                          V                                  2                  ,                  Lo                                ′                            ⁡                              (                t                )                                              =                                                    C                                  2                  ,                  1                                ′                            ⁢                              sin                ⁡                                  (                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      c                                        ⁢                    t                                    )                                            ⁢                              sin                ⁡                                  (                                      Δϕ                    ⁡                                          (                      t                      )                                                        )                                                      +                                          C                                  2                  ,                  2                                ′                            ⁢                              sin                ⁡                                  (                                      4                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      c                                        ⁢                    t                                    )                                            ⁢                              cos                ⁡                                  (                                      Δϕ                    ⁡                                          (                      t                      )                                                        )                                                      +                                          C                                  2                  ,                  3                                ′                            ⁢                              sin                ⁡                                  (                                      6                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      c                                        ⁢                    t                                    )                                            ⁢                              sin                ⁡                                  (                                      Δϕ                    ⁡                                          (                      t                      )                                                        )                                                      +            …                                              (        5        )                                                          ⁢                                            V                              2                ,                Lo                            ″                        ⁡                          (              t              )                                =                                    C                              2                ,                1                            ′                        ⁢                          sin              ⁡                              (                                  2                  ⁢                  π                  ⁢                                                                          ⁢                                      f                    c                                    ⁢                  t                                )                                      ⁢                          sin              ⁡                              (                                  Δϕ                  ⁡                                      (                    t                    )                                                  )                                                                        (        6        )            
Then, V″1,Lo(t) and V″2,Lo(t) are transmitted to analogous adder 16 and added, and a modulation depth is adjusted to comply with an equation (7):C′1,1=C′2,1B(J3(φc)−J1(φc))=−BJ2(φc)  (7)
When V″1,Lo(t) and V″2,Lo(t) comply with the equation (7), V″1,Lo(t) and V″2,Lo(t) are added to obtain a simple sine wave expressed by an equation (8):
                                          V                          Sum              ,              Lo                                ⁡                      (            t            )                          =                                                                              V                                      1                    ,                    Lo                                    ″                                ⁡                                  (                  t                  )                                            +                                                V                                      2                    ,                    Lo                                    ″                                ⁡                                  (                  t                  )                                                      ⇒                                          V                                  Sum                  ,                  Lo                                            ⁡                              (                t                )                                              =                                                                                          C                                          1                      ,                      1                                        ′                                    ⁢                                      cos                    ⁡                                          (                                              2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          c                                                ⁢                        t                                            )                                                        ⁢                                      cos                    ⁡                                          (                                              Δϕ                        ⁡                                                  (                          t                          )                                                                    )                                                                      +                                                      C                                          2                      ,                      1                                        ′                                    ⁢                                      sin                    ⁡                                          (                                              2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          c                                                ⁢                        t                                            )                                                        ⁢                                      sin                    ⁡                                          (                                              Δϕ                        ⁡                                                  (                          t                          )                                                                    )                                                                                  ⇒                                                V                                      Sum                    ,                    Lo                                                  ⁡                                  (                  t                  )                                                      =                          D              ⁢                                                          ⁢                              cos                ⁡                                  (                                                            2                      ⁢                      π                      ⁢                                                                                          ⁢                                              f                        c                                            ⁢                      t                                        -                                          Δϕ                      ⁡                                              (                        t                        )                                                                              )                                                                                        (        8        )            
After passing through a signal-demodulating process circuit, a signal becomes the sine wave. Finally, the sine wave is transmitted to a phase lock circuit 18 to be demodulated into an angle variation Δφ(t) required. As a result, sense data of a sensor is obtained.
According to the abovementioned derivation, the equation (7) is established to satisfy the equation (8), and a value of the modulation depth is very important. As a result, φc is limited to 2.2, which is not flexible enough to design the optical sensing system of PMDI. In addition, the upper limit of a carrier frequency is limited, thereby affecting a bandwidth of the sensor. Theoretically, the upper limit of the bandwidth of the sensor is 1/10 fc. Thus, it is difficult for the circuit architecture to design an integrated circuit (IC) since each element of the circuit has complex design and the whole circuit area required is too large to be encapsulated in a chip. Specifically, two band-pass filters 14 and 14′ required have complex design and large volumes since the design requires the information of a single frequency (fc, 2fc). Additionally, high-frequency harmonic waves of the equations (3) and (5) are completely filtered out by the analogous band-pass filters 14 and 14′, otherwise the accuracy of an output signal is influenced.
In practice, each band-pass filter has a design of as high as ten or more order which means that the band-pass filter requires ten or more operation amplifiers and larger capacitors and resistors. The demand limits a possibility to use the architecture to realize an IC. Besides, the circuit architecture requires high linearity of the analogous multipliers 12 and 12′. If the analogous multipliers have nonlinearity, harmonic waves appear in the result of the analogous multipliers to result in distortion. Also, the circuit architecture requires pure sine waves with frequency of fc and 2fc. Either an external instrument or an oscillator can generate the sine wave. The instrument and the oscillator consume the cost and cannot provide pure sine waves with frequency of fc and 2fc, which results in distortion of the demodulated signal. In other words, the angle variation Δφ(t) is precisely obtained by merely using a high-linearity analogous multiplier, a pure sine wave generator and a high-order band-pass filter, which is the present bottleneck for designing a micro integrated circuit. And, the problems of too large areas of resistors and capacitors, high design complexity, high power consumption and bad linearity exist. Accordingly, how to reduce circuit elements required should be solved whereby the circuit elements are realized in a limited chip area without affecting the normal function of the circuit. To overcome the abovementioned problems, the present invention provides a periodically resetting integration angle demodulation device and a method using the same, so as to solve the afore-mentioned problems of the prior art.